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arXiv:1911.04799 · Physical Review A

Towards practical security of continuous-variable quantum key distribution

Cosmo Lupo

Published Aug 31, 2020• 18 citations
arXivHTMLPDF

Abstract

Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.

DOI
10.1103/physreva.102.022623

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Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I investigate these issues in detail, and discuss experimentally friendly workarounds to assess the security of CV QKD. The aim of this paper is to show that there are hidden and unsolved issues and to indicate possible partial solutions. To provide a complete and rigorous mathematical security proof is out of the scope of this contribution.
Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.
Quantum key distribution allows two parties to establish an encryption key that, by the laws of physics, no other party can have knowledge on and therefore enables information-theoretic communication security. In particular, quantum key distribution with continuous variables (CV-QKD) represents a way to exercise quantum cryptography at a high technological readiness level taking advantage of the leading-edge technological infrastructure provided by the telecom industry. The review by Fabian Laudenbach et al. (article number 1800011) provides a detailed introduction to the mathematical tools and relations required for the security analysis of CV-QKD and particularly deals with the effects of necessarily imperfect hardware components.
In recent years, discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) has gained traction due to its practical advantages: cost-effectiveness, simple state preparation, and compatibility with existing communication technologies. This work presents a security analysis of DM-CV-QKD against general sequential attacks, including finite-size effects. Remarkably, our proof considers attacks that are neither independent nor identical, and makes no assumptions about the Hilbert space dimension of the receiver. To analyse the security, we leverage the recent generalised entropy accumulation theorem and the numerical methods based on quasi-relative entropy. We also develop a novel dimension reduction technique which is compatible with the entropy accumulation framework. While our analysis reveals significant finite-size corrections to the key rate, the protocol might still offer advantages in specific scenarios due to its practical merits. Our work also offers some insights on how future security proofs can improve the security bounds derived in this work.
Quantum Key Distribution (QKD) provides a method for securely sharing a secret key between two distant parties, Alice and Bob, by leveraging the principles of quantum mechanics. This thesis focuses on Continuous-Variable (CV) QKD, a variant of QKD where information is encoded in the quadrature components of coherent light states, allowing for efficient and cost-effective detection using homodyne or heterodyne receivers. The thesis is divided into three main parts: an introduction to quantum cryptography concepts, the presentation of a CV-QKD protocol, and a detailed security proof of the protocol against different types of attacks. The security proof considers both finite and infinite symbol transmission and tackles various eavesdropping attacks, including individual, collective, and coherent attacks. The use of Gaussian states and operations provides a promising approach to enhance QKD security, particularly in the context of practical quantum cryptography. The final sections provide a mathematical framework for the optimization of secure key rates and strategies for addressing the photon-number cutoff assumption in practical implementations.
Modern security proofs of quantum key distribution (QKD) must take finite-size effects and composable aspects into consideration. This is also the case for continuous-variable (CV) protocols, which are based on the transmission and detection of bosonic coherent states. In this paper, we refine and advance the previous theory in this area providing a more rigorous formulation for the composable key rate of a generic CV-QKD protocol. Thanks to these theoretical refinements, our general formulas allow us to prove more optimistic key rates with respect to previous literature. Published by the American Physical Society 2024
Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond 707070km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.